What is the integral of 7x^3cos(2+x^4)-8x^3e^{2+x^4} ?

The integral of 7x^3cos(2+x^4)-8x^3e^{2+x^4} is 7/4 sin(2+x^4)-2e^{2+x^4}+C

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integral of 7x^3cos(2+x^4)-8x^3e^{2+x^4}

\int 7 x^{3} cos (2 + x^{4}) - 8 x^{3} e^{2 + x^{4}} d x

\frac{7}{4} sin (2 + x^{4}) - 2 e^{2 + x^{4}} + C

Solution steps

\int 7 x^{3} cos (2 + x^{4}) - 8 x^{3} e^{2 + x^{4}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7 x^{3} cos (2 + x^{4}) d x - \int 8 x^{3} e^{2 + x^{4}} d x

\int 7 x^{3} cos (2 + x^{4}) d x = \frac{7}{4} sin (2 + x^{4})

\int 8 x^{3} e^{2 + x^{4}} d x = 2 e^{2 + x^{4}}

= \frac{7}{4} sin (2 + x^{4}) - 2 e^{2 + x^{4}}

Add a constant to the solution

= \frac{7}{4} sin (2 + x^{4}) - 2 e^{2 + x^{4}} + C

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What is the integral of 7x^3cos(2+x^4)-8x^3e^{2+x^4} ?
The integral of 7x^3cos(2+x^4)-8x^3e^{2+x^4} is 7/4 sin(2+x^4)-2e^{2+x^4}+C